M. Nafi Toksöz

VELOCITY AND ATTENUATION OF SEISMIC WAVES IN TWO‐PHASE MEDIA: PART I. THEORETICAL FORMULATIONS

The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and the matrix material. For long wavelengths the problem is formulated in terms of scattering phenomena in an approach similar to that of Ament (1959). The displacement fields, expanded in series, for waves scattered by an “effective” composite medium and individual inclusions are equated. The coefficients of the series expansions of the displacement fields provide a relationship between the elastic moduli of the effective medium and those of the matrix and inclusions. The expressions are derived for both solid and liquid inclusions in a solid matrix as well as for solid suspensions in a fluid matrix. Both spherical and oblate spheroidal inclusions are considered. Some numerical calculations are carried out to demonstrate the effects of fluid inclusions of various shapes on the seismic velocities in rocks. I...

Diffraction tomography and multisource holography applied to seismic imaging

Seismic tomography is emerging as an imaging method for determining subsurface structure. When the view‐angle coverage is limited and the scale of the medium inhomogeneities is comparable with the wavelength, as is often true in geophysical applications, the performance of ordinary ray tomography becomes poor. Other tomographic methods are needed to improve the imaging process. Here we study diffraction tomography and multisource holography and evaluate their performances for surface reflection profiling (SRP), vertical seismic profiling (VSP), and cross‐hole measurements. Theoretical formulations are derived for two‐dimensional geometry in terms of line sources along a source line and line receivers along a receiver line. The theory for diffraction tomography is based on the Born or Rytov approximation. The performances of diffraction tomography and multisource holography are evaluated by examining the information coverage in the spatial frequency domain and by numerical examples. Multisource holography,...

Velocity variations and water content estimated from multi-offset, ground-penetrating radar

The common midpoint (CMP) processing technique has been shown to be effective in improving the results of ground-penetrating radar (GPR) profiling. When radar data are collected with the CMP multioffset geometry, stacking increases the signal-to-noise ratio of subsurface radar reflections and results in an improved subsurface image. An important aspect of CMP processing is normal-moveout velocity analysis. Our objectives are to show the effect of multiple velocity analyses on the stacked radar image and particularly, to demonstrate that this velocity information can also be used to determine subsurface water content. Most GPR surveys are very limited in spatial extent and assume that within the survey range, radar velocity structure in the shallow subsurface can be adequately approximated by a single velocity function in data processing. In this study, we show that variation in radar velocity can be quite significant and that the stacked profile improves as the number of velocity analysis locations is increased. Interval velocities can be calculated from the normal moveout velocities derived in the CMP velocity analysis. With some reasonable assumptions about subsurface conditions necessary for radar propagation, interval velocity can be converted to an estimate of volumetric water content. Therefore, by collecting GPR data in the multioffset CMP geometry, not only is the radar profile improved but it also allows for an interpretation of subsurface variation in water content. We show the application of these techniques to multioffset GPR data from the Chalk River test area operated by Atomic Energy of Canada Limited.

Elastic wave propagation in a fluid‐filled borehole and synthetic acoustic logs

The propagation and dispersion characteristics of guided waves in a fluid‐filled borehole are studied using dispersion curves and modeling full‐wave acoustic logs by synthetic microseismograms. The dispersion characteristics of the pseudo‐Rayleigh (reflected) and Stoneley waves in a borehole with and without a tool in the center are compared. Effects of different tool properties are calculated. The effect of a rigid tool is to make the effective borehole radius smaller. As an approximation, dispersion characteristics of the guided waves in a borehole with a tool can be calculated as a purely fluid‐filled borehole with a smaller effective radius. Theoretical waveforms (microseismograms) of elastic waves propagating in a borehole are calculated using a discrete wavenumber integration. With an appropriate choice of parameters, our results look similar to the acoustic waveforms recorded in a limestone and a shale formation. Several factors affect the shape of an acoustic log microseismogram. The effective rad...

How fast is rupture during an earthquake? New insights from the 1999 Turkey Earthquakes

We report that during the two devastating 1999 earthquakes in Turkey, rupture propagated over a large part of the nearly 200km long fault zone at supershear speed approaching 5km/s. We present observations and modeling which confirm the original inference of supershear rupture during the Izmit earthquake and we show that supershear rupture also occurred during the Duzce earthquake. We show that the rupture velocity measured—about √2 times the shear wave velocity—is the value predicted by theoretical studies in fracture dynamics. We look for clues to explain these observations.

Experimental Determination of Elastic Anisotropy of Berea Sandstone, Chicopee Shale and Chelmsford Granite

We used the ultrasonic transmission method to measure P-, SH-, and SV-wave velocities for Chelmsford granite, Chicopee shale, and Berea sandstone in different directions up to 1 000 bars confining pressure. The velocity measurements indicate these three rocks are elastically anisotropic. The stiffness constants, dynamic Young’s moduli, dynamic Poisson’s ratios, and dynamic bulk moduli of the three rocks were also calculated. The elastic constants, together with velocity measurements, suggest that: (1) elastic anisotropy is due to the combined effects of pores or cracks and mineral grain orientation, and (2) elastic anisotropy decreases with increasing confining pressure. The residual anisotropy at higher confining pressure is due to mineral grain orientation.

Space and Time Evolution of Rupture and Faulting during the 1999 İzmit (Turkey) Earthquake

We use the records of the ground motion obtained at near-fault accelerometers to study the space and time evolution of rupture and faulting during the Izmit earthquake. We find that the rupture propagated at the sub-Rayleigh speed of about 3 km/sec on the western and eastern segments of the fault, but that the central segment (Izmit-Sapanca Lake-Sakarya), nearly 50 km long, broke at the supershear speed of about 4.8 km/sec. This value, within the range of uncertainties, is the one theoretically predicted ( \(\sqrt{2}V_{\mathrm{S}}\) ) in fracture dynamics for stable shear crack growth at intersonic speed. We infer an average fault slip of about 2.9 m over a total rupture length of about 150 km, with the largest values (of up to 6 m) occurring in the Golcuk area to the west and in the Sakarya region to the east. The strong-motion data also indicate that the slip diminished gradually to the west beyond the Hersek peninsula over about 30 km, whereas it stopped abruptly at depth at the termination of the eastern (Karadere) segment. The slip duration is between 2 and 4 sec, except in the hypocentral area, which slipped in about 1 sec. The seismic moment inferred is about 2.5 × 10 20 N m.

Spatial orientation and distribution of reservoir fractures from scattered seismic energy

Wepresentthedetailsofanewmethodfordeterminingthereflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations we have made from 3D finite-difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fracture corridors impart a coda signature, which is a ringing tail of scatteredenergy,toanyseismicwaveswhicharetransmittedthrough or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1 the difference in angle between the orientation of the fractures and the acquisition direction, 2 the fracture spacing, 3 the wavelength of the illuminating seismic energy, and 4 the compliance, or stiffness, of the fractures. This coda energy is most coherent when the acquisition direction is parallel to the strike of thefractures.Ithasthelargestamplitudewhentheseismicwavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. Our method uses surface seismic reflection tracestoderiveatransferfunctionthatquantifiesthechangeinan apparent source wavelet before and after propagating through a fracturedinterval.Thetransferfunctionforanintervalwithnoor low amounts of scattering will be more spikelike and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. When a 3D survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows us to identify subsurface areas with high fracturing and to determine the strike of those fractures.Wecalibratedthemethodwithmodeldataandthenapplied ittotheEmiliofieldwithafracturedreservoir.Themethodyielded results which agree with known field measurements and previously published fracture orientations derived from PS anisotropy.

Numerical studies of back-arc convection and the formation of marginal basins

Abstract Marginal basins that occur behind island arcs display geological and geophysical features that imply an extensional origin and a spreading mechanism, possibly driven by the heating of the basin floor from below. The origin and evolution of these basins appear to be associated with the subduction process of the oceanic lithosphere. The mechanism we propose for the formation and spreading of marginal basins is the convective flow induced in the mantle by the subducting slab. This convective current brings hot mantle material to the base of the lithosphere behind island arcs. The combination of material upwelling, heating of the lithosphere and flow induced tension initiates spreading and the formation of marginal basins. Quantitative investigation of this mechanism has been carried out utilizing numerical calculations using both constant and variable viscosity models. Numerical results indicate that the induced flow can generate a 1 km topographic rise and a tensile stress of about 100 bars. Together with the thinning of the lithosphere due to heating, this induced current is probably sufficient to generate inter-arc spreading at about 5–10 million years after the initiation of subduction. The horizontal scale of the spreading center obtained from the numerical models is also consistent with the observations over many marginal basins.

Electroseismic investigation of the shallow subsurface: Field measurements and numerical modeling

Recent studies have demonstrated that electroseismic phenomena in porous media have the potential to detect zones of high fluid mobility and fluid chemistry contrasts in the subsurface. However, there have only been a few field studies of these phenomena since they were first observed 60 years ago. None of these studies were able to support observations with an explicit comparison to results of full waveform modeling. In this paper, we demonstrate that the electroseismic phenomena in porous media can be observed in the field, explained, and modeled numerically, yielding a good agreement between the field and the synthetic data. We first outline the design of our field experiment and describe the procedure used to reduce noise in the electroseismic data. After that, we present and interpret the field data, demonstrating how and where different electroseismic signals originated in the subsurface. Finally, we model our field experiment numerically and demonstrate that the numerical results correctly simulate arrival times, polarity, and amplitude variation with offset behavior of the electroseismic signals measured in the field.